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 IntegerPart

 http://functions.wolfram.com/04.04.21.0005.01

 Input Form

 Integrate[IntegerPart[t], {t, 0, a}] == (1/2) (2 a - 1 - IntegerPart[a]) IntegerPart[a]

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[SubsuperscriptBox["\[Integral]", "0", "a"], RowBox[List[RowBox[List["IntegerPart", "[", "t", "]"]], RowBox[List["\[DifferentialD]", "t"]]]]]], "\[Equal]", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "a"]], "-", "1", "-", RowBox[List["IntegerPart", "[", "a", "]"]]]], ")"]], " ", RowBox[List["IntegerPart", "[", "a", "]"]]]]]]]]

 MathML Form

 0 a int ( t ) t 1 2 ( 2 a - int ( a ) - 1 ) int ( a ) t 0 a int t 1 2 2 a -1 int a -1 int a [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[SubsuperscriptBox["\[Integral]", "0", "a_"], RowBox[List[RowBox[List["IntegerPart", "[", "t_", "]"]], RowBox[List["\[DifferentialD]", "t_"]]]]]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "a"]], "-", "1", "-", RowBox[List["IntegerPart", "[", "a", "]"]]]], ")"]], " ", RowBox[List["IntegerPart", "[", "a", "]"]]]]]]]]

 Date Added to functions.wolfram.com (modification date)

 2001-10-29

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